Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
202 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D199 |
| commutator, socle, cosocle | C23×C199 | C23 |
| Fitting | #95×C199 | C2 |
| prime radical | C23×D199 | C22 |
| hypercenter | #95 | D199 |
| hypocenter | C199 | #393 |
| LCS | G ▷ C23×C199 ▷ C199 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic398 | C2 | semidirect |
| 4. C199⋊#95 | C2 | semidirect |
| 5. #95×C199 | C2 | semidirect |
| 19. C22×D199 | Q8 | semidirect |
| 52. C199 | #393 | semidirect |
| 58. #95 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic398 | 2 |
| C2×(C2×D199)⋊C4 | 2 |
| C199⋊#95 | 2 |
| #95×C199 | 2 |
| #393 | 199 |